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A general Chevalley formula for semi-infinite flag manifolds and quantum K-theory

  • Cristian Lenart [1] ; Satoshi Naito [2] ; Daisuke Sagaki [3]
    1. [1] State University of New York

      State University of New York

      City of Albany, Estados Unidos

    2. [2] Tokyo Institute of Technology

      Tokyo Institute of Technology

      Japón

    3. [3] University of Tsukuba

      University of Tsukuba

      Japón

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  • Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 30, Nº. 3, 2024, págs. 1-44
  • Idioma: inglés
  • DOI: 10.1007/s00029-024-00924-8
  • Enlaces
  • Resumen

    • We give a Chevalley formula for an arbitrary weight for the torus-equivariant Kgroup of semi-infinite flag manifolds, which is expressed in terms of the quantum alcove model. As an application, we prove the Chevalley formula for an anti-dominant fundamental weight for the (small) torus-equivariant quantum K-theory QKT (G/B) of a (finite-dimensional) flag manifold G/B; this has been a longstanding conjecture about the multiplicative structure of QKT (G/B). In type An−1, we prove that the so-called quantum Grothendieck polynomials indeed represent (opposite) Schubert classes in the (non-equivariant) quantum K-theory QK(SLn/B); we also obtain very explicit information about the coefficients in the respective Chevalley formula.

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